n(3n+17)=930

Solution for n(3n+17)=930 equation:

n(3n+17)=930

We move all terms to the left:

n(3n+17)-(930)=0

We multiply parentheses

3n^2+17n-930=0

a = 3; b = 17; c = -930;
Δ = b2-4ac
Δ = 172-4·3·(-930)
Δ = 11449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11449}=107$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-107}{2*3}=\frac{-124}{6}
=-20+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+107}{2*3}=\frac{90}{6}
=15
$